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Golay Sequences for FDMA Wake-Up Signal Transmission

This contribution proposes a method using existing Golay sequences to address the significant increase in PAPR when wake-up signals are transmitted using FDMA. The Golay sequences provide a low PAPR solution for FDMed wake-up signals.

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Golay Sequences for FDMA Wake-Up Signal Transmission

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  1. OOK Waveform for FDMA • Date: 2018-05-07 Authors:

  2. Introduction • In the previous meeting, FDMA transmission is proposed [1]: • Each 20 MHz channel only contains one 4 MHz sub-channel for wake-up signal transmission • In this contribution, we propose a method based on existing QPSK Golay sequences to remedy the significant PAPR increase when WUSs are FDMed [1]: IEEE 802.11-17/1625r6

  3. CP CP Problem Statement CP CP CP CP CP CP Overlapping in time • The PAPR can be significantly high since the ON signals on different channels overlap in time in case of FDMA • Intractable problem because • There may be 1, 2, 3, or 4 active channels • The active channel locations in frequency could be different • LDR and HDR waveforms can also be different (e.g., CP size etc.) HDR CP CP Time HDR CP CP Time LDR CP CP Time HDR Time 2s many combinations for a given time period

  4. CP CP CP CP CP CP CP CP CP Transmitter Block Diagram (HDR) Manchester-coded bit (0) IDFT CP CP CP CP CP CP CP 7 Channel 1 0 Time • For HDR, FDMA can be supported through a single IDFT operation • This representation is not different than generating single-channel mask–based MC-OOK (length of 7) waveforms, shifting them in frequency, and then summing them up every 2 s • We use this representation for the following discussions • Question: How to choose the sequences { such that the PAPR of the signal is below a certain level, e.g., 3 dB? Manchester-coded bit (1) 1 7 Channel 2 Time 1 CP+ Manchester-coded bit (1) 7 Channel 3 Time Manchester-coded bit (0) 0 Time 7 Channel 4 2s

  5. Golay Complementary Sequences • A sequence pair is called a complementary sequence if • , • where is the length of and , and are the inverse Fourier • transforms of and , respectively • Because of the definition, the PAPR of the inverse Fourier transform of a Golay sequence is always bounded by 3 dB • The sequences and the construction methods have been known since 1961* and have been heavily-used in IEEE 802.11ad/ay IDFT ** *Golay, M. (April 1961). "Complementary series". IEEE Transactions on Information Theory. 7 (2): 82–8 *https://en.wikipedia.org/wiki/Complementary_sequences **Matthew G. Parker, Kenneth G. Paterson, ChinthaTellambura, “Golay Complementary Sequences”, 2004

  6. Generating a Length 7 Sequence with nulled DC tone (Single Channel) • The Golay sequences can be generated through concatenations and zero padding of the sequences in a pair • For example, and construct a Golay pair. • Hence, and also construct another pair • This property can be useful to generate a Golay sequence with a nulled DC tone, e.g., • We can use the same construction method to remedy the PAPR problem Frequency 3 1 3

  7. Concatenating Golay Sequences(Multiple Channels) 1/2 A Golay sequence Channel 4 Channel 1 Channel 2 Channel 3 • The figure above shows some examples of several channelization • The PAPR is always less than or equal to 3 dB even if there is a non-contiguous mapping Frequency A Golay sequence Frequency A Golay sequence Frequency

  8. Concatenating Golay Sequences(Multiple Channels) 2/2 • Other cases can also be generated with several Golay construction methods* Channel 4 Channel 1 Channel 2 Channel 3 A Golay sequence Frequency A Golay sequence Frequency *Matthew G. Parker, Kenneth G. Paterson, ChinthaTellambura, “Golay Complementary Sequences”, 2004

  9. CP CP Handling FDMed LDR and HDR WUSs CP CP Option 1 for LDR: Time 4s Option 2 for LDR: 2s • If we use Option 2, the design for LDR and HDR can be unified and the IDFT durations are aligned CP CP CP CP Time HDR Time LDR CP CP CP CP CP CP Time 2s

  10. CP CP CP CP CP TX Diagram for FDMed LDR and HDR WUSs CP CP CP CP CP CP CP Ch #1 (HDR) 0 Time Manchester-coded bit: 0 1 IDFT 7 Channel 1 Ch #2 (HDR) Time Manchester-coded bit: 1 1 7 Channel 2 Ch #3 (LDR) CP CP CP CP Time CP+ Manchester-coded bit: 1 7 Channel 3 Ch #4 (HDR) 0 Time Manchester-coded bit: 0 2s 7 Channel 4 Rate: 1 symbol/2s Not Golay sequences but low PAPR Example tone indices for : [-3:3]-48 Example tone indices for : [-3:3]-16 Example tone indices for : [-3:3]+16 Example tone indices for : [-3:3]+48

  11. Simulation Assumptions • We simulate 5 different cases considering various FDMed WUSs with HDR and LDR (the results for different cases are given in appendix) • AP: 80 MHz sample rate • PA: Rapp model with the smoothness factor of 3, 4x oversampling • WURx: • Envelope detector (i.e., samples the accumulated the sum of absolutes of I- and Q- branches), 5th order Butterworth filter, ideal synchronization • We compare the MC-OOK proposals in the following contributions for HDR and LDR with the Golay sequences are given in Slide 10 • Option 1: Golay-based (QPSK) • Option 2: LDR/HDR: IEEE 802.11-18/0479r2 (256 QAM) • Option 3: LDR: IEEE 802.11-18/0421r0/HDR: IEEE 802.11-18/0492r0 (BPSK) • Option 4: LDR/HDR: IEEE 802.11-18/0421r0 (BPSK) • We apply phase rotations for the channels as described in IEEE 802.11ac for 492, 479, and 421 • Extra phase rotations for different channels are not needed for Golay sequences

  12. Numerical Analysis (2 HDRs, 2LDRs) Legacy SYNC HDR HDR LDR HDR Time domain signal

  13. Numerical Analysis (2 HDRs, 2LDRs) Legacy SYNC HDR HDR LDR HDR Time domain signal

  14. Numerical Analysis (2 HDRs, 2LDRs) Legacy SYNC HDR HDR LDR HDR Time domain signal

  15. PAPR Results (2 HDRs, 2LDRs)

  16. PAPR Results for Different Cases • The probability of sample power being 9.55 dB, 12.39 dB, and 10.77 dB higher than the average is 0.2 for Option 2, 3, and 4, respectively, in some cases (see appendix for details) • The instantaneous power is less than 6.67 dB above the average for Option 1 (Golay sequences) for all cases with .99 probability

  17. Spectral Growth under PA Impairment • Option 1 (Golay) causes less spectral growth for OBO = 5 dB as compared to other options

  18. BER Results Golay-based WUS is robust Similar performance w/o PA • When the samples are clipped heavily because of PA, the sum of absolute values can decrease and WUSs can interfere with each other • Saturation can degrade the BER performance at WURx (e.g., Option 3) • Golay-based WUS provides robustness against PA non-linearity by minimizing the fluctuation in time for FDMed OOK symbols

  19. Conclusion • The PAPR can be significantly large when WUSs are FDMed • Without taking any precautions, it can reach 10-13 dB or higher, which limits the coverage range of 802.11ba in some regions • The PAPR minimization for FDMed WUSs is an intractable problem due to the large number cases possible in an FDM scenario • The phase rotations in IEEE 802.11ac cannot address all cases and they are a function of the sequence • A scalable solution is needed • Existing Golay sequences can address the PAPR issue as the corresponding signals are always bounded by 3 dB • We show that the PAPR gain can reach more than 3 dB in some cases • Golay sequences are publicly available • Known since 1960s • Heavily-used in 802.11ad/ay • Used for PAPR minimization, coding, etc. in academic studies

  20. Appendix

  21. PAPR 6.4 dB [1] 3.6 dB [2] Mean power While PAPRs are 3.4 and 0.6 dB for 2 s duration for the waveform in 492 and 479, respectively, they increase by 3 dB for a measurement at 4 s duration since there is no energy for the OFF durations in the corresponding waveforms This means that if the ON period is generated via a Golay sequence, the PAPR will be limited to 6 dB for a measurement which covers both ON and OFF durations [1]: IEEE 802.11-18/0492r0 [2]: IEEE 802.11-18/0479r2

  22. PAPR Results – Case 1

  23. PAPR Results – Case 2

  24. PAPR Results – Case 3

  25. PAPR Results – Case 4

  26. PAPR Results – Case 5

  27. BER (Case 3) Golay-based WUS is robust Golay-based WUS is robust

  28. SP • Do you agree that the method of OOK waveform generation based on Golay sequences described in the Slide 10 can be included in the 802.11ba spec as an example for implementing the frequency domain multiplexed WUS? • Y • N • A

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